{
 "cells": [
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-04-15T08:26:01.711068Z",
     "start_time": "2025-04-15T08:26:01.697936Z"
    }
   },
   "cell_type": "code",
   "source": [
    "# 导入必要的库\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "plt.rcParams.update({\n",
    "    'font.size': 14,          # 全局字体大小\n",
    "    'axes.titlesize': 16,     # 标题字体大小\n",
    "    'axes.labelsize': 14,     # 坐标轴标签字体大小\n",
    "    'xtick.labelsize': 12,    # x轴刻度字体\n",
    "    'ytick.labelsize': 12,    # y轴刻度字体\n",
    "    'legend.fontsize': 20     # 图例字体\n",
    "})\n",
    "# 初始化设置\n",
    "plt.rcParams['font.sans-serif'] = ['KaiTi']  # 中文字体\n",
    "plt.rcParams['mathtext.fontset'] = 'stix'     # 数学字体\n",
    "# 负数\n",
    "plt.rcParams['axes.unicode_minus'] = False\n",
    "\n"
   ],
   "id": "da4839b8e4384e32",
   "outputs": [],
   "execution_count": 16
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-04-15T08:26:03.338093Z",
     "start_time": "2025-04-15T08:26:03.328097Z"
    }
   },
   "cell_type": "code",
   "source": "",
   "id": "fbff0e4bded71958",
   "outputs": [],
   "execution_count": 16
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-04-15T09:10:36.442482Z",
     "start_time": "2025-04-15T09:10:36.425941Z"
    }
   },
   "cell_type": "code",
   "source": "",
   "id": "2a982246d0fa23f1",
   "outputs": [],
   "execution_count": 43
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-04-15T09:13:51.612602Z",
     "start_time": "2025-04-15T09:13:51.468433Z"
    }
   },
   "cell_type": "code",
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# 示例1：非特征向量变换\n",
    "A1 = np.array([[-1, 1], \n",
    "               [2, -2]])\n",
    "w1 = np.array([2, 3])\n",
    "p1 = A1 @ w1  # 矩阵乘法\n",
    "\n",
    "# 示例2：特征向量变换\n",
    "A2 = np.array([[0.5, 1], \n",
    "               [0, 2]])\n",
    "w2 = np.array([2, 3])\n",
    "p2 = A2 @ w2  # 结果为(4,6)，即2倍原向量\n",
    "\n",
    "# 绘制示例1图形\n",
    "fig1, ax1 = plt.subplots(figsize=(6, 6))\n",
    "\n",
    "# 示例1绘图\n",
    "ax1.quiver(0, 0, w1[0], w1[1], angles='xy', scale_units='xy', scale=1, color='b', label='$w\\;(2,3)$')\n",
    "ax1.quiver(0, 0, p1[0], p1[1], angles='xy', scale_units='xy', scale=1, color='r', label='$p\\;(1,-2)$')\n",
    "\n",
    "# 设置坐标轴范围\n",
    "ax1.set_xlim(0, 3)\n",
    "ax1.set_ylim(-3, 3)\n",
    "\n",
    "# 添加网格\n",
    "ax1.grid(True)\n",
    "\n",
    "# 设置标题\n",
    "ax1.set_title(\"非特征向量的变换\", fontsize=12)\n",
    "\n",
    "# 添加图例\n",
    "ax1.legend(loc='upper left')\n",
    "\n",
    "plt.tight_layout()\n",
    "plt.show()\n",
    "\n"
   ],
   "id": "cff8923275440a1f",
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 600x600 with 1 Axes>"
      ],
      "image/png": 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\n"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "execution_count": 53
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-04-15T09:14:33.505867Z",
     "start_time": "2025-04-15T09:14:33.409524Z"
    }
   },
   "cell_type": "code",
   "source": [
    "\n",
    "# 绘制示例2图形\n",
    "fig2, ax2 = plt.subplots(figsize=(6, 6))\n",
    "\n",
    "# 示例2绘图\n",
    "ax2.quiver(0, 0, w2[0], w2[1], angles='xy', scale_units='xy', scale=1, color='b', label='$w\\;(2,3)$', width=0.01)\n",
    "ax2.quiver(0, 0, p2[0], p2[1], angles='xy', scale_units='xy', scale=1, color='r', label='$p\\;(4,6)$', width=0.005)\n",
    "\n",
    "# 设置坐标轴范围\n",
    "ax2.set_xlim(0, 6)\n",
    "ax2.set_ylim(0, 8)\n",
    "\n",
    "# 添加网格\n",
    "ax2.grid(True)\n",
    "\n",
    "# 设置标题\n",
    "ax2.set_title(\"特征向量的变换（λ=2）\", fontsize=12)\n",
    "\n",
    "# 添加图例\n",
    "ax2.legend(loc='upper left')\n",
    "\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ],
   "id": "9804ad38c5caae90",
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 600x600 with 1 Axes>"
      ],
      "image/png": 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\n"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "execution_count": 56
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-04-18T09:59:07.806660Z",
     "start_time": "2025-04-18T09:59:07.782648Z"
    }
   },
   "cell_type": "code",
   "source": "",
   "id": "1ce605349dcea1cf",
   "outputs": [],
   "execution_count": null
  },
  {
   "metadata": {},
   "cell_type": "code",
   "outputs": [],
   "execution_count": null,
   "source": "",
   "id": "79255039901011d6"
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
